WASHINGTON — Picking up momentum toward a historic overhaul of the country’s health-care system, Democrats yesterday unveiled the final version of President Obama’s $940 billion plan, setting up a dramatic final House vote on Sunday.

In a day filled with fast-paced developments, the White House announced that Obama was scrubbing his planned trip to Indonesia and Australia this weekend to stay in DC for the finish.

“He wants to be here for the history,” House Speaker Nancy Pelosi said.

Many of the overhaul’s provisions will start immediately, while others don’t take effect for years.

A provision preventing insurance companies from denying coverage for a pre-existing condition takes effect in six months for children, although it wouldn’t cover all adults until 2014.

A tax on “Cadillac” health plans got rolled back until 2018 under union pressure.

The delayed implementation of key elements allowed lawmakers to lower the cost of some provisions, or ease the pain of groups about to be taxed, while ratcheting up fines and fees to pay for reform.

The fact that the estimated cost came in under $1 trillion provided another argument for leaders to use on wavering conservative Democrats, who worry about the bill’s high cost and risk of political blowback.

The bill trims the deficit by cutting $500 billion in Medicare spending and raking in additional revenues with a new tax on investment income — about 1 percent higher than the Senate bill.

A new 10 percent tax on indoor tanning salons would raise almost $3 billion.

Many of the major insurance reforms begin in 2014, including provisions requiring most Americans for the first time to purchase insurance, and face penalties if they don’t.

Republicans continued to howl about a bill that many of them called a government takeover, and ripped the process Democrats were using to jam the legislation through.

The House voted down a Republican resolution, 222-203, to block the use of a tactic to “deem” the Senate-passed bill to have passed the House even though it was not subjected to a vote. The ploy is intended to shield Democrats from having to explain a vote for unpopular provisions that will be wiped out of the bill’s final version.

Republicans on the Ways and Means Committee warned that the bill could require the IRS to hire 16,000 additional agents to enforce the new rules.

“It is a dangerous expansion of the IRS’s power and reach into the lives of virtually every American,” said Rep. Dave Camp (R-Mich.).

Another provision provides $2 billion to expand health coverage for the territories of Puerto Rico, Guam, the US Virgin Islands and the Northern Mariana Islands.

The bill would also provide federal direct lending for student loans, and one portion provides a carve-out protecting the lending role of the state Bank of North Dakota — though a sponsor, Sen. Kent Conrad (D-ND), denied it was a special deal.

At a Capitol press conference, Pelosi was in full fighting form.

“There is no limit to what the other side will do to protect the insurance companies,” she said.

The final deal drops Obama’s just-announced plan for a watchdog agency with the power to block premium rate hikes. Aides said the change couldn’t overcome budget rules to make it through the Senate.

A Senate GOP aide said other provisions that got included would be subject to challenge on the Senate floor.